Almost degenerate Riemann surfaces and the focusing Nonlinear Schrodinger equation as a model for anomalous wave generation

The rogue (anomalous) waves in nature are actively studied now. The generation of such giant waves is an essentially non-linear phenomena, and the focusing Nonlinear Schrodinger equation is treated as one of the basic mathematical models. In the spatially periodic setting anomalous waves correspond to special solutions associated with almost degenerate spectral curves. In this seminar results obtained in collaboration with P.M. Santini will be presented. We show that these special theta-functional solutions admits a simple explicit approximation by elementary functions. P.G. Grinevich was supported by RSF grant No 18-11-00316.